The correct option is D. 20° + 120°k or 40° + 120°k. This is the correct general solution to the given equation.
The equation 2 sin (3x) -√3=0 can be written as sin(3x) = √3/2
To find the general solution, we need to solve for x in the range of 0° to 360° using the reference angle of 30°. We can apply the formula as shown below: sin(30°) = 1/2sin(60°) = √3/2sin(90°) = 1
Thus, we can rewrite the equation as sin(3x) = sin(60°). This means that 3x = 60° + 360°k or 180° - 60° + 360°k, where k is an integer.
We can then solve for x by dividing by 3. So, x = 20° + 120°k or 40° + 120°k.
Therefore, the general solution to the equation is given by: x = 20° + 120°k or 40° + 120°k, where k is an integer.
Choice A: 30° + 360°k
This is not a solution to the given equation.
Choice B: 60° + 180°k
This is not a solution to the given equation.
Choice C: 60° + 360°k
This is not a solution to the given equation.
Choice D: 20° + 120°k or 40° + 120°k
This is the correct general solution to the given equation.
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will give brainlest!Solve the triangle, Round answers to the nearest tenth.
Answer:
C
Step-by-step explanation:
Answer:
Angle B should be 37°
Step-by-step explanation:
All i fugured out was the angle measure, which should be 90+53=143 and 180-143=37°, I’m just not sure what the other stuff means/needs.
1.A house worth $250,000 has an coinsurance clause of 90 percent. The owners insure the property for $191,250. They then have a fire that causes $80,000 in damage. How much money will they receive from insurance?
2.A house worth $180,000 has a coinsurance clause of 75 percent. The owners insure the property for $101,250. They then have a loss that results in a $50,000 claim. How much money will they receive from insurance?
1. Multiply the value of the house by the percent:
250,000 x 0.9 = 225,000
Divide the amount the owner insured by the clause amount:
191,250/225,000 = 0.85
Multiply that by the amount of damage:
0.85 x 80,000 = 68,000
They will receive $68,000
2. Follow the same steps as above:
180,000 x 0.75 = 135,000
101,250 / 135,000 = 0.75
0.75 x 50,000 = 37,500
They will receive $37,500
Answer:
1. They will receive $72,000 in insurance.
2. They will receive $37,500 in insurance.
Step-by-step explanation:
1.Given that the coinsurance is 90 percent.
For the fire that caused a $80,000 in damage, 90 percent of $80,000 will be received in insurance.
90 percent of $80,000 will be received in insurance
90 percent of $80,000 = 0.9 * 80000
= 72,000
Therefore, they will receive $72,000 in insurance
2. The coinsurance is 75 percent, given that they have a loss that results in a $50,000 claim.
they will received 75 percent of $50,000
75 percent of $50,000 = 0.75 * 50000
= 37.500
Therefore, they will receive $37,500
The $25.00 shirt costs the store $20.00. Find the markup rate.
Answer:
25%
Step-by-step explanation:
plsss help find the domain and range please thank you god bless you x
Answer:
Domain : -1 ≤ x ≤ 3Range : 6 ≤ y ≤ 27Step-by-step explanation:
The domain is the set of possible x-values.
The range is the set of possible y-values.
Domain : -1 ≤ x ≤ 3
Range : 6 ≤ y ≤ 27
Find the volume of a cone with a height of 12 and a radius of 4 if it's only a third full.
Answer: V= 67.0199
Step-by-step explanation: I'm not sure if that's the answer but to find volume you use V=3.14*r^2 h/3. After putting in the heigh and radius to the equation you get 201.06 and since only 1/3 is full i multiplyed it by that and got 67.0199
Suppose you want to represent a triangle with sides of 12 feet, 15 feet, and 18 feet on a drawing where 1 Inch - 3 feet How long should the sides of the triangle be in inches? 12 feet should be inches. 15 feet should be 18 feet should be inches.
In linear equation, The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.
What in mathematics is a linear equation?
An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation.
The above is sometimes called a "linear equation in two variables" where x and y are variables. Equations in which the variable is power 1 are called linear equations. axe+b = 0 is a one-variable example where a and b are real numbers and x is a variable.
A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.
Then, 1 feet of original triangle = 1/2 inch on drawing.
Now, the sides of the triangle on the drawing are
12 feet = 1/2 * 12 = 6 in
12 feet = 1/2 * 16 = 8 in
12 feet = 1/2 * 18 = 9 in
Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches..
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If the weight of packages is multiplied by 6/5 (fraction) the result is 24.5 pounds. What is the weight of the package (in pounds)?
The weight of the package in pounds is 24.42 pounds.
According to the question,
We have the following information:
If the weight of packages is multiplied by 6/5 (fraction) the result is 24.5 pounds.
First, we will convert this fraction into a number with a decimal point.
So, we have:
6/5 = 1.2
Now, let's take the weight of the packages to be x pounds.
So, we have the following expression:
1.2x = 24.5
x = 24.5/1.2
(1.2 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 20.42 pounds
Hence, the weight of the package in pounds is 20.42 pounds.
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Rebecca believes that the sum of 3 + (-53) is 8.9 Kenneth thinks the sum is -27. Who is correct?
Answer:
They both are not correct.
Step-by-step explanation:
3+(-53) = -50 not -27 or 8.9
fill in the blank to make the two fractions equivalent. 3/4 = ?/24
Answer:
3/4 = 18/24
Step-by-step explanation:
4x6 is 24 so jus times 3 by 6 and get 18
so the answer is 18
What should the exponent be for 11 a.m?
Answer:
-1
Step-by-step explanation:
this should be the exponent. Hope this helps you :)
Question 14 of 16
Identify the domain of the function shown in the graph
A. All positive integers
B. All real numbers
6. All positive real numbers
D. X>=0
B, because you would just assume the line continues forever on both sides.
PLEASE HELP I have no idea what I'm doing!!! I'm giving 20 points!!
Answer:
A
B
C
Step-by-step explanation:
100% correct answers
Answer:
C
Step-by-step explanation:
The temperature in Minneapolis at 9 a.m. was −8°F. By noon, the temperature had risen by 8°F.
What was the temperature at noon?
Answer: 0
Add the number 8 to -8, because 8 is how much the temperature rose.
-8 + 8 = 0.
The temperature in Minneapolis is now 0 Fahrenheit.
Hope this helps you!
I don't understand this at all
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
Use the information you found in Part 1 to help you answer Part2.Type of Ball football basketball baseball softballCost perBall$8.00 $9.00 $7.00 $5.00TotalNumber ofBalls(from Part1)1. When Mrs. Weeks bought all of the baseballs and softballs, she paidfor them using four $100.00 bills. How much change did she receive?2. Write expressions that include parentheses and order of operations toshow how to find the answer. Show your work.3. After school began, Mrs. Weeks realized that she needed morebasketballs and footballs. If she spent $135.00 on basketballs and$48.00 on footballs, how many more balls did she purchase?4. Write expressions the include parentheses and order of operations toshow how to find the answer. Show your work.
Solution:
The number of footballs given is
\(f=8\)The equation for basketball will be
\(\begin{gathered} basketball=2f+2 \\ b=2(8)+2 \\ b=16+2 \\ b=18 \end{gathered}\)The equation for baseball will be
\(\begin{gathered} baseball=5f-4 \\ baseball=5(8)-4 \\ baseball=40-4 \\ baseball=36 \end{gathered}\)The equation for softball will be
\(\begin{gathered} s=\frac{1}{2}baseballs+6 \\ s=\frac{1}{2}(36)+6 \\ s=18+6 \\ s=24 \end{gathered}\)Part 2:
The table will be used to solve part 2
What are the measures of line segments AB and AC?
Answer:
So you want to know the number of a b and c?
Step-by-step explanation :
Answer:
a = 90°
b = 60°
c = 30°
Step-by-step explanation:
hope u understood
can you help me now
How many different ways can 4 children be ordered in a line?.
Answer:
There are approximately 24 ways to order them to form a line
a triangle has a side length of 5.4 and 7 x x=
Answer:
D. 8.8
Step-by-step explanation:
As the pythagorean theorem.
A² + B² = C²,
5.4 × 5.4 + 7 × 7 = C²,
29.16 + 49 = C²,
78.16 = C²,
8.8 ≈ C
11
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
Answer:
28 cmStep-by-step explanation:
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)
or you can use an expression
4 * √49 = 28
Solve the equation.
4/7 = 10/X
x=
Answer:
x = 17.5
Step-by-step explanation:
4/7 = 10/X
We can use cross products to solve for x
4*x = 7 * 10
4x = 70
Divide by 4
4x/4 = 70/4
x = 17.5
Answer:
17.5
Step-by-step explanation:
\( \frac{4}{7} = \frac{10}{x} \\ \)
Use cross multiplication.
4x = 7 × 10
4x = 70
Divide both sides by 4.
x = 70/4
x = 17.5
4.
Clients are served in a process with two resources. The
capacities of the resources are 1.1 and 0.93 clients per hour.
Demand occurs at the rate 0.75 clients per hour.
What is the implied utilizati
Answer:
Step-by-step explanation:
The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).
The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.
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4. The side lengths of a triangle are x, x – 9, and 2x + 3. If the perimeter of the triangle is 46 cm, what is the value of x?
HELPPP
Answer:
x=13
Step-by-step explanation:
perimeter equals the sum of sides of triangle
perimeter= x+x-9+2x+3
46=4x-6
46+6=4x
4x=52
x=52/4
x=13
Complete the table and then graph the function
Since y = x + 13 you have only to replace x with values on the table:
for x = -10 => y = -10 + 13 = -3for x = -7 => y = -7 + 13 = 6for x = -6 => y = -6 + 13 = 7for x = -5 => y = -5 + 13 = 8Now we have the coordinates of the points (x, y):
(-10, -3)(-7, 6)(-6, 7)(-5, 8)Now draw the points and connect them. I hope this helped.
Subtract 11 from 111 in base two
The difference of the given numbers with base 2 is 100₂.
The given expression is 111₂-11₂.
Most students can do simple subtraction by the time they get to Secondary school. The operation is technically a base-10 operation in which you "carry" and "give" sets of 10. The "carry" and "give" rules are the same for other number bases; the difference is that the sets are the sets for the number base. For base 2, the sets would be 2s.
In the first step, we simply do the operation: 1-1
111₂
-11₂
___
0₂
In the next step, we do the operation 1-1
111₂
-11₂
___
00₂
Finally, let's do the operation 1-0
111₂
-11₂
___
100₂
Therefore, the difference of the given numbers with base 2 is 100₂.
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Find the length of the arc in terms of pi
Answer:
\(8\pi\)Solution,
Radius= 12
Theta= 120
Length of arc AB:
\( \frac{120}{360} \times 2\pi(12) \\ = \frac{120}{360} \times 24\pi \\ = 8\pi\)
Hope this helps...
Good luck on your assignment...
Solve the inequality -2c – 5 > -7 and graph the solution.
An aircraft carrier can travel 450 km in the same time a container ship travels 300 km. If the aircraft carrier was travelling 5 km/h faster what was the speed of the container ship? (answer is a rational expression)
Answer:
10 km/hr
Step-by-step explanation:
The aircraft carrier and the container ship both took 30 hours to travel their respective distances. If you divide both numbers by 30, you find that their differences is 5. We can tell that the aircraft carrier traveled 450 ÷ 30 = 15 km/hr and the container ship traveled at a speed of 300 ÷ 30 = 10 km/hr. The aircraft carrier traveled 5 km/hr faster. So, we can tell the container ship traveled at 10 km/hr.
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Select the correct answer. In which of the scenarios can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful? A. As the number of cigarettes smoked in a day increases, the risk for lung cancer increases. B. As the age of an infant increases, the height of the infant increases. C. As the number of vehicles in a city increases, the amount of pollution in the city increases. D. As the concentration of salt in water increases, the density of water increases. E. As the number of calls made by a cell phone increases, the cell phone bill amount increases. Reset Next
Answer:
In Option A, we can see that the reverse may not be true as the increase in the risk for lung cancer may not necessarily mean an increase in cigarette smoked in a day. For example, high risk of lung cancer may be due to high exposure to asbestos dust too.
In Option B, again we can see that the reverse may not be true as an increase in the height of an infant does not necessarily mean that the age of the infant is increasing too. For example the infant may have a rapid gain in height even if the age is not increasing as rapidly.
In Option C, too, that an increase in the amount of pollution in a city does necessarily mean that the number of vehicles in the city has increased. For example, this increase in pollution may be due to the establishment of a high pollution causing industry in the city or in it's vicinity.
Likewise, in Option D, an increase in the density of water does not necessarily mean that the concentration of salt in the water has increased.
Only in Option E do we see a possible reverse dependence happening because an increase in the phone bill amount does usually mean an increase in the number of calls made by the cell phone.
So, in the given list of Options only in Option E can we reverse the dependent and independent variables while keeping the interpretation of the slope meaningful.
Step-by-step explanation:
Choose the item that does NOT have a measurable volume. Air, a water bottle, a box of crackers, a dollar bill
Answer:
Air
Step-by-step explanation: